Determine the length of the third side of a triangle from the choices provided if the first two sides measure 10 and 12.
A. 30
B. 22
C. 24
D. 15
To determine the length of the third side of a triangle, you can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the first two sides measure 10 and 12, so the sum of their lengths is 10 + 12 = 22. The length of the third side must be greater than 22.
Looking at the choices provided, the length of the third side is not 30 (A) or 15 (D) since both of these values are greater than 22.
The length of the third side is also not 24 (C) since 10 + 12 = 22 is equal to the given length.
Therefore, the only remaining option is B. 22.
that's wrong
Apologies for the error in my previous response.
To determine the length of the third side of a triangle, you can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this case, the first two sides measure 10 and 12. Therefore, the length of the third side must be greater than |10 - 12| = 2 and less than 10 + 12 = 22.
Looking at the choices provided, the length of the third side is not 30 (A) since it is greater than 22.
The length of the third side is not 15 (D) either since it is less than 22.
The length of the third side is not 24 (C) since it is equal to the sum of the first two sides, which violates the triangle inequality theorem.
Therefore, the correct answer is B. 22, as it falls within the valid range of possible lengths for the third side.